Multiplicative operations in BP∗BP
Douglas C. Ravenel · Pacific Journal of Mathematics · 1975
One of the present computational difficulties in complex cobordism theory is the lack of a known algebra splitting of BP*BP, the algebra of stable cohomology operations for the Brown-Peterson cohomology theory, analogous to the splitting isomorphism MU*MU » MU*(pt) <g) Swhere S is the Landweber-Novikov algebra.S has the added advantage of being a cocommutative Hopf algebra over Z.This paper does not remove this difficulty, but we will show that the monoid of multiplicative operations in BP*BP, (i.e.those operations which induce ring endomorphisms on BP*X for any space X) 9 which we will denote by Γ{BP), has a submonoid analogous to the monoid of multiplicative operations in S.